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4.M1
Numbers and Operations
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4.M.1a
identify verbally and in writing the place value for each digit in whole numbers up to 1,000,000 and decimals between 0 and 1, up to thousandths;
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4.M.1b
identify and generate equivalent representations for the same number by decomposing and composing the whole number up to 1,000,000;
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4.M.1c
judge the size of fractions by using benchmarks, e.g., 0, 1/2, 1; and use the terms greater than, less than, or equal to or appropriate mathematical symbols >, <, or = to compare a fraction to the benchmark;
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4.M.1d
identify and describe using their own words whole numbers according to their characteristics including primes, composites, and perfect squares;
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4.M.1e
use models and symbols to recognize and generate equivalent forms of fractions, mixed numbers, and decimals;
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4.M.1f
use models to represent division problems as the inverse of multiplication, as partitioning, or as successive subtraction and describe the meaning of remainders;
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4.M.1g
use models and equivalence to add and subtract fractions with like denominators of 12 or less;
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4.M.1h
use models to add and subtract decimals through thousandths;
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4.M.1i
divide two-digit whole numbers by one-digit divisors;
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4.M.1j
use the inverse relationships of addition and subtraction, and multiplication and division to solve problems and verify solutions;
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4.M.1k
use estimation to make predictions and check the reasonableness of result;
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4.M.1l
identify, compare, and order the relative position of fractions and decimals on a number line;
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4.M.1m
demonstrate mastery in sums to 20 and related subtraction facts and multiplication through 12X12 and related division facts;
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4.M2
Algebra
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4.M.2a
use models and words to describe, extend, and generalize repeating, number, and growing patterns and relationships;
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4.M.2b
represent and analyze repeating, number, and growing patterns using words, tables, and graphs;
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4.M.2c
represent and describe mathematical relationships using algebraic expressions, equations, or inequalities with mathematical symbols;
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4.M.2d
apply order of operations and the commutative and associative properties of addition and multiplication to numeric expressions;
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4.M.2e
use and interpret variables, mathematical symbols, and properties of addition and multiplication (e.g., commutative, associative, and the distributive property) to write and simplify mathematical expressions and sentences;
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4.M.2f
write and solve algebraic equations or inequalities using variables that represent problem situations;
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4.M.2g
identify and describe patterns of change to make predictions that identify the relationship represented in a table or graph.
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4.M3
Geometry
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4.M.3a
identify, draw representations, and describe the relationships between and among points, lines, line segments, and rays using appropriate mathematical tools; e.g., intersecting, parallel, and perpendicular lines;
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4.M.3b
identify and draw representations of right angles, obtuse angles, and acute angles using appropriate mathematical tools;
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4.M.3c
identify and draw congruent figures using appropriate mathematical tools;
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4.M.3d
describe the results of subdividing, combining, and transforming shapes;
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4.M.3e
find the distance between locations of points along horizontal and vertical lines of a coordinate grid;
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4.M.3f
predict and describe transformations (i.e., translation, reflection, and rotation) to show that two shapes are congruent;
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4.M.3g
identify and describe line and rotational symmetry in two-dimensional shapes and designs;
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4.M.3h
identify geometric solids which could be composed of other solids;
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4.M4
Measurement
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4.M.4a
recognize and describe that measurements are approximations;
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4.M.4b
measure with accuracy using both customary and metric systems of measurement;
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4.M.4c
recognize that the area is the measure of the space enclosed by a two-dimensional figure and that angles are figures made by two rays with the same endpoint;
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4.M.4d
determine the possible dimensions of rectangles when the area is constant;
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4.M.4e
estimate measurements of perimeter, area, and angle size;
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4.M.4f
use standard tools and units to include measure of perimeter and area of two-dimensional figures;
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4.M.4g
describe strategies to determine the perimeter and area of right triangles;
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4.M.4h
describe strategies for estimating the area of irregular shapes;
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4.M.4i
solve problems involving perimeter and areas of rectangles;
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4.M.4j
know the process for counting coins and bills using standards monetary notations;
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4.M5
Data Analysis and Probability
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4.M.5a
describe how data collection methods affect the information that is gathered to address a question;
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4.M.5b
identify the median of a data set and describe what it indicates about the data set;
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4.M.5c
use the median, mode, and range to compare and contrast the characteristics of related data sets;
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4.M.5d
select the appropriate data representation form for a diverse set of investigations and justify the choice in each case;
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4.M.5e
identify the likelihood of an event occurring as impossible, equally likely, and certain. Recognize the numerical values of 0 (impossible) and 1 (certain);
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4.M.5f
conduct experiments to determine experimental probability of an event occurring for a given number of trials (no more than 12 trials), using models;
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4.M.5g
list and count all possible combinations using one member from each of several sets;
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